Heretofore, various light-deflectors in which mirrors are resonance-driven have been proposed. In general, a resonance type light-deflector is characterized in that, comparing to a light scanning optical system using a polygonal rotating mirror such as a polygon mirror, the light-deflector can be made compact to an large extent, and the consumption power thereof can be reduced, and there exists no face tangle in theory, and particularly, a light-deflector comprising Si single-crystal manufactured by a semiconductor process theoretically has no metal fatigue, and is excellent in durability (Japanese Patent Application Laid-Open No. S57-8520).
In the meantime, in the resonance type reflector, there is a problem that, since a scanning angle of the mirror changes in sine-wise in principle, an angular velocity is not constant. To correct this characteristic, several techniques have been proposed.
For example, in Japanese Patent Application Laid-Open Nos. H9-230276, H9-230277, H9-230278, and H9-230279, an arcsin lens is used as an image-forming optical system (image-forming lens), so that a constant velocity scanning is realized on a scanned surface.
Further, in Japanese Patent Application Laid-Open No. 2003-279879, two pieces of deflection reflecting surfaces are driven by sine oscillations of mutually different oscillation cycles, thereby synthesizing sine waves and realizing an approximate constant angular velocity drive within a scanning range.
Further, in U.S. Pat. No. 4,859,846, by using a resonance type deflector having a basic frequency and an oscillation mode of a frequency being three times the basic frequency, an approximate chopping wave drive is realized.
In electro-photography such as a laser beam printer, a laser light is scanned on a photosensitive body so as to form an image. At that time, the scanning velocity of the laser light is preferably a constant velocity on the photosensitive body. Hence, in a light-scanning means used in the electro-photography, it is generally that, after the light-deflector performs the scanning, an optical correction is carried out.
For example, in the light-scanning optical system using the polygonal rotating mirror, in order to convert a light flux reflected and deflected at the constant velocity by the deflection reflecting surface into the constant scanning on the photosensitive body, an image-forming lens called a fθ lens is used.
Further, in the light-scanning optical system using the light-deflector for performing a sine oscillation, in order to change a light flux in which the angular velocity changes in a sine wise into the constant velocity scanning on the photosensitive body, an image-forming lens called an arcsin lens is used.
However, the arcsin lens has a problem in that the size of a beam spot of the laser light on the photosensitive body changes at the time of the optical scanning correction. In general, in the image-forming apparatus, there exist allowable upper and lower limits to the size of the beam spot allowable according to a required image quality. Therefore, in the angular velocity of the laser light emitted from the light-deflector, there exists an allowable value in the fluctuation width of the angular velocity. Here, the upper and lower limits of the angular velocity are denoted by θ′max, and θ′min, respectively.
Now, in the light-deflector performing the sine oscillation, a displacement angle θ and the angular velocity θ′ can be represented by the following formulas:θ=θo sin (ωt)  (Formula 1)θ′=θo ω cos (ωt)  (Formula 2)provided that θo is the maximum displacement angle, and ω is the number of angular oscillations. At this time, the relations ofθ′max=θo ω  (Formula 3)θ′min≦θo cos (ωt)  (Formula 4)are established. FIG. 17 explains these states. In FIG. 17, the time range satisfying the above described formulas in the vicinity of t=0 is within a range of:−cos−1 (θ′min/θoω)≦ωt≦−cos −1 (θ′min/θo ω)  (Formula 5)and the maximum usable deflection angle θeff satisfying this condition and an effective time teff which is a usable time in one cycle become as follows:θeff=θo sin (cos−1 (θ′min/θ′max))  (Formula 6)teff=2 cos −1 (θ′min/θ′max)/ω  (Formula 7)
For example, if θ′ is allowable up to ±20% for a reference angular velocity, it becomesθ′min:θ′max=0.8:1.2  (Formula 8)and thereby the maximum usable deflection angle θeff and the effective time teff become as follows:θeff=θo sin (cos−1 (0.8/1.2))=0.7454θo  (Formula 9)teff=2 cos−1 (0.8/1.2)/ω=1.6821/ω  (Formula 10)In this way, there is a problem that the conventional resonance type light deflector is unable to fully obtain the maximum usable deflection angle θeff and the effective time teff as large values.
Further, there is a problem that, since the resonance type deflector has the same angular velocity in moving back and forth, when making a single side scanning, the time effectively acquired for the scanning becomes short.
Further, there is a problem that, when a plurality of deflectors are used for correcting these problems, the structure becomes complicated.
Further, there is a problem that since the mirror has to maintain a desired flatness even at the time of driving, its rigidity has to be enhanced so as to restrain the deformation of the mirror. In the light-deflector performing the sine oscillation as in the Formula 1, the angular acceleration θ″ of the mirror can be given as follows.θ″=−θoω2 sin (ωt)  (Formula 11)
In the above example, the angular acceleration becomes the maximum value at both ends of the scanning, and the maximum value is:θ″max=θoω2 sin (cos−1 (0.8/1.2))=0.7454θoω2  (Formula 12)
Further, there is a problem that, when assembling a movable element and a torsion spring, it takes a lot of troubles, and moreover, it is easy to generate an assembly error.
Further, there is a problem that, when trying to make the moment of inertia of the movable element large, it makes miniaturization difficult. In the resonance type light-deflector having two or more of movable elements, it is most desirable that the moment of inertia of the movable element on which a light-deflecting element is arranged is the smallest. However, when attempting to form movable elements and torsion springs by working a piece of plate, in order to make the moment of inertial large, a plate having a large area is required. This becomes a barrier for miniaturization. Further, in case the movable elements and the torsion springs are formed by the semiconductor process, a larger size of a foot print becomes a cause of cost increase.
Further, there is a problem that, when the movable elements are connected in series by the torsion springs, it is easy to generate not only torsion, but also a flexure oscillation mode.
FIG. 18 is a model for explaining a flexure oscillation mode. Movable elements 1601 and 1602 are connected by a torsion spring 1611, and the movable element 1602 and a support portion 1621 are connected by a torsion spring 1612. Such a system generally has two flexure oscillation modes. The oscillation mode form at this time is shown in FIGS. 19A and 19B. FIG. 19A shows an inphase flexure oscillation mode at a lower frequency, and FIG. 19B shows a reverse phase flexure oscillation mode at a higher frequency. It is desirable that these oscillation modes are controlled as much as possible.